We have closed content on the site which should be available only for authorized users depends from roles.
1) Please advise whether Google/SE bots can sees the content, index it and show it in search results (images, videos, etc)? How content is protected from this?
2) installing of SE counts on the site to see customers behavior will compromise protection of closed content?
When a bot crawls your site it does so without any user authentification, it is not logged in to your site, and so it can only see what a guest user arriving at your site through a web browser could see.
If you have content that is only visible to certain roles, then bots cannot access that content.